Well, I'm not sure what the process is for short stories vs novels, but I imagine it's similar. For a novel, you would find several agents who represent your type of story, and send them query letters. Query letters have a format, and agents read a TON of them each day, so be sure to research the query letters in general and the agents in particular you wish to query.
http://queryshark.blogspot.com is a great resource for how to and how NOT to write query letters for novels, and it's a fun read in general.
For information on publishing short stories specifically, you could post a thread at the Nanowrimo forums -
http://www.nanowrimo.org/en/forums - or just look around there and see what others have posted on the subject. There is a ton of information there on what to do after you finish a story/novel.
One thing I know you do NOT do for novels is send your story straight to an editor. The chain is author-agent-editor. Editors do not like receiving unsolicited manuscripts. This may not apply if you are trying to get published in something like a magazine, though.
Hope that sheds some light on it.